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Considering the use and practicality of equal temperment in standard tuned guitars, I started measuring and calculating cent values for any given semi-tone and arrived at miniscule dimensions that make a difference in pitch, but are really hard to compensate for.
Given the build specs of one of my commissions, I decided to try to exact my intonation and dial in a more accurate scale layout. Checking some of my calculations against manufactured instruments revealed a surprisingly high level of inaccuracy. First of all, I will say that most people can't tell the difference in 3 cents off pitch, Unless I had the tuner in front of me pointing it out, I can't tell either. But what I did determine from testing these other instruments with a greater discrepancy in pitch was a complete difference in overall tone and sound of each guitar. This made me wonder and figure that among the various characteristics and approaches each builder utilizes in the construction of a guitar, this factor also adds the trademark sound and tone to different guitars. Intonation practices and the method with which frets are marked and set allow for subtlies in tone. Several innovators on this topic have devised methods they feel are more precise, but require extensive work to the nut and saddle, some even the frets themselves.
Now I could just be wrong, but I checked this formula against several brands and found they all varied flat or sharp by as much as 7 cents off,
depending on which fret it is, you may not be able to compensate to pitch. One cent being 1/1000th of a semi-tone is pretty hard to evaluate and correct. I doubt seriously if any of this is even relevant to playing and building a guitar, but I find myself wondering how I can cut any more accurately than I do. Not that I'm concerened, I think my practices have born decent sounding and close to pitch instruments, so in other words, everyone that builds a guitar is apt to have a different tone escape the box and I think this has a little to do with it. Could be that a little fall off "flat" translates to a woodier sound, and a more bell like chiminess is "sharper", maybe it's too early in the morning and my coffees' cold again.
I know that construction and bracing, top thickness and such all are more contributing factors in individual tone differences, but I think this could have a little to do with certain tonal variances.
Anyone want to measure out their frets after the fact and see how they run as compared to the measurements given for that scale?
I spend a good deal of time on this part of my builds, any comments on how others view this and their methods of installation?

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Nehemiah Covey
www.coveysacoustics.com

The first question is what are you going to measure a cent value with. The common digital tuners with a series of LED light bars have a +/-4cent accuracy tolerance. Meaning at any given reading the meter can be off by 4cent in either direction. Most top end chromatic tuners have a +/-1cent accuracy tolerance. Meaning at any given reading the meter can be 1cent off in either direction. A Peterson strobe is accurate to with in +/- 1/10th of a cent. Meaning it can be off 1/10th of a cent in either direction. This is very important to know the tolerance of the meter because as you go from one string to the next these tolerances interact and affect unison.

Most musically un-trained human ears notice difference in pitch at +/-8 cent. Most trained musicians at +/-2cent and those that claim perfect pitch have a hard time dealing with a guitar.

My opinion on intonating a commissioned guitar is get it with in acceptable range for a trained musician's ear. It is near impossible and will end up turning your gray matter to jelly trying to be dead on perfect pitch intonation and the guitar does not play to perfect temperament in the first place.

Those are very good points Michael, I have been using a peterson 490 strobe, and you're right the accuracy is claimed 1/10th , which is close enough, but my thoughts were on common practices in just how close and by what means others go about referencing fret locations.
Lately here in my area I have had a number of people jumping on the intonation wagon, asking for finer tuned isntruments and talking about equal temperament and the flaws in this system. Seems there are so many variables embodied in the guitar as a whole, this is just an impossible notion.
But it prompted me to research the feasiblity of spot on pitch, and I 've determined these folks need to play a different instrument. I have come up with a method that works very similarly to the Feiten system, or Earvanna's method, but still it requires about 48 hours more work and several hundred dollars extra just to make it worth my time.
Grand Concert Piano, that's the only place you will find this type of accuracy, and only if it's tuned properly.
Thanks for the input Michael.

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Nehemiah Covey
www.coveysacoustics.com

Cutting frets slots, the scale division process used, the accuracy of the cutting process, the accuracy of fret dressing, the accuracy of nut shapeing and instalation. The list goes on and on and on. It would be interesting to tale a series of guitars that most say sound dark in tone, a series that most say sound bright and shimmering in tone and a series that most say sound balanced and compare the open/12/12 hamonic intonation and half step by half step intonation. just to see what we would find out about them.

That's essentially just what I did Michael,
I had 3 people bring their guitars to my shop and we played them and rated them as , in our terms, woodier to brighter. 5 instruments in total 4 dreads and 1 R/W OM, the dreads were all mohagany, and all 5 were spruce topped in a 25-1/2" scale.. The 3 guitars that had a darker or woodier tone all indicated a tendency towards flat pitch, by some 1 to 7 cent variance.
The 2 brighter guitars were just the opposite. But by smaller margins sharper than spot on pitch, 1 to 4 cents. So I concluded what my first post touched on, I think this has a little to do with the resulting tone of any particular instrument. But I would have to test many many guitars to say for sure it works this way.

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Nehemiah Covey
www.coveysacoustics.com

I like the way you think Nehemiah. You just got my brain going in a whole new direction. Not that I know what the heck I'm talking about but isn't one cent equal to 1/100th of a semitone, and an octive being 1200 cents?

Post more on your findings, this is interesting. Thanks for the brain food.

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"After forty-nine years of violin building, I have decided that the search for a varnish is similar to the fox hunt. The fun is in the hunt."
Jack Batts Maker and Repairer of Fine Violins

It is important to remember that the 12 tone equal temperment scale we use and which the tuner measures is a compromise developed to allow the piano to play in "sort of in tune" or "equally out of tune" in all keys.
It is not an absolute and only approximates the natural ratios between the root note and fifths etc.

Compensated nut systems like the BF and earvana generally atttenpt two things
-improving string deflection innotation issues on the lower frets
-sweetening the intervals between notes on common chords in open positions especially.

But in the end it is still compromises, perfect pitch is an illusion

Good stuff folks!

This is a site where you can test your sound card, your own ability to distinguish pitch and a bunch of other stuff. Don't know if it appeared here before, but it's worth a look.

http://www.audiocheck.net/

Pat

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formerly known around here as burbank
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http://www.patfosterguitars.com

Chuck, You are exactly right!, my bad, I actually didn't see that I had one too many "0"s in there. I would not have seen that really. Thanks for pointing it out.
ONE/ONEHUNDRETH of a semi tone.
To add to this information, let's assume a guitar is reading 7 cents off at the 12th fret of a 24.9" scale. Knowing that the correct "in-pitch" measurement to the 13th fret is .699" or 45/64" , 7 cents off then equals a discrepancy of .048" or 3/64". That's why I posted this, to see how critical others are about spotting the frets and maintaining that scribed mark as measured. Even given the equal temerament of standard guitar, it's not hard to be off by quite a bit as you factor in cutting and marking.
I scribe my fret marks and then cut initially with a saw width of .008" and afterwards resaw at .023" for the fret fitting, after chamfering the slots with a small file. Otherwise I can't see the scribe under the .023" saw blade.
Maybe I'm anal about it, but it works for me.

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Nehemiah Covey
www.coveysacoustics.com

Yeah Nehemiah
Gotta get those fret slots cut in the right position or you do not have a hope.
Actually an error of the magnitude you mention would be quite obvious visually as well as accoustically.
The first board I slotted myself was out by about half that up around the 14th and I found it visually unacceptable and rejected it (and it was on a weissenborn so pitch was not the issue)

Actually , the tuning is stretched a little sharp towards the highest notes and dropped a little flat on the very lower. Apart from other reasons ,the human ear inadequacy demands this ,so that it ' sounds ' in tune



Careful Jeff , As a Piano Tuner/Technician , I've found those claiming 'perfect pitch' to be quite offended when told otherwise.
After 40 years on the job , I still use a tuning fork ( kept at a constant temperature next to my body ).

Differing fretting pressure alone , easily alters pitch on a guitar , even if you think you have the intonation close. A good guitarist 'plays 'the guitar in tune with the pressure of his fretting fingers


Craig Lawrence
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CRAIG LAWRENCE of AUSTRALIA
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double posted

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CRAIG LAWRENCE of AUSTRALIA
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Triple posted

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CRAIG LAWRENCE of AUSTRALIA
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3rd time is charm

Yes Craig fretting pressure is a huge effect and also plucking strength.
Hit a low E string hard and the pitch showing on the tuner goes all over the place.

I prefer the accuracy of a sawing template like L.M.I. and Stewmac sell. These templates are made on C.N.C and avoid that human error. Sawing a line to a scribed mark is always going to be dubious without a proper cutting jig .L.M.I. have recently updated their manual slotting jig ( and it's cheaper than their older model ! )


Craig Lawrence
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CRAIG LAWRENCE of AUSTRALIA
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Yep ! And that will vary on what guage strings you are using . The lighter the guage set , the more variance in pitch.


Craig Lawrence
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CRAIG LAWRENCE of AUSTRALIA
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I understand the intrigue with intonation accuracy, as an eternal problem or riddle you may hope to improve upon. There are a few things I think you should consider in your problem solving though.

First, no a human ear can't detect a change of a few cents in a single note. It's not a matter of skill or training, but of human anatomy. From the flow of vibrations through the cochlea, to hairs on the basilar membrane, our ears are simply not made to differentiate such narrow bands of frequency. This limitation of the human ear is often brought up to defend a disregard of such small discrepancies, but really that's not entirely justified unless you're playing a series of individual notes.

Once there are two or more notes played in unison or harmony, we can certainly hear much smaller differences. In upper octaves especially, we can easily detect differences of less than a single cent. We hear this disharmony not directly as a difference in frequency however, but in pulses or beats as the waves go in and out of phase with each other. So yes, precision is nice, but now we get in to a lot of bigger obstacles with the guitar.

First of course is temperament. Unless you're playing limited chords in a single key, that's a problem that can not be solved within a 12 tone scale. It is what it is, and regardless of what any innovative systems claim to deliver, it is something we are stuck with on guitars, pianos, organs, etc. That's the #1 obstacle, throwing some intervals off as much as 16 cents from what would be a pure, beatless harmony.

Second is the setup. A bad setup or a poorly cut nut can easily throw notes 3 or 4 cents out of where we would intend them to be. A good setup (especially a well refined nut height) is the first step for a builder to bring their instruments in better harmony. It is also the most often overlooked, or at least poorly executed part of a guitar's construction. A bad setup can outweigh any precision in fret placement, causing far greater discrepancies than a fret even .030" out of place.

Third is the player. Even with a well setup instrument, players can easily shift a note 3 or 4 cents depending on how they fret. This can be a very useful tool in the hands of a skilled and intentional player, or a curse for those less skilled.

Accuracy of fret placement I would place around 4th on the list. So long as you have reasonable accuracy of .003"-.004", it's not going to make or break the intonation. Any discrepancies within this range will be greatly overshadowed by the factors listed above. A nut that is .003" too high will literally have in the range of 10x the impact that the first fret being .003" out of place would cause. So don't get too bent out of shape about insane accuracy of fret slots. If you can stay in a reasonable range of ±.003"-.004", you're doing fine and none of those errors (unless compounded) will add up to much in the end.

Intentional offsets are a different ball game. To be quite honest I feel that although most come from good intentions, many are a misguided effort to solve a symptom of a problem. Most are overcompensating for bad setups. Some are simply futile attempts to improve certain ratios, though only those ignorant of temperament will claim to be able to improve one ratio without harming another. Unless you're going fretless or to something like Partch's 43 tone scale, it's just not going to happen.

And don't be fooled in to thinking that a piano is in any way an example of perfection or "better in tune". To the contrary, they are more restricted than the guitar. The violin is fully flexible and can be perfect. The piano is perfectly rigid, and is locked in to whatever restrictions the tuner left it with. The guitar on the other hand, is semi-flexible. A good guitarist can train to bend and stretch certain fingers in certain chord shapes, and actually improve the temper of chords as they play. Not quite so flexible as a violin, but not so restrained as a piano.

So you can do all you want with precision frets or specialized offsets. In my opinion though, that is entirely chasing the wind. Good setup, good setup, good setup. Those guitars you measured with 7 cent discrepancies had a really really bad setup.

Then equal to good setup, is a good player with good technique and a good ear. Players often want technicians to magically fix a problem which is ultimately in the player's hands during performance. Wishing for any proprietary compensation systems or tuning method to take care of everything, is no different from wanting a special pair of shoes that will let you win the race without having to work out. Players often don't want to accept their part of the responsibility, but unless they do they will never play in tune. Period.

As a builder or setup tech, you should not be searching for any precision that doesn't exist. You should be looking at the likely range of error for a particular player or setup (maybe try to find the reasonable ±2¢ window), the shoot for the middle. Provide the player with a good brush and canvas to fit their style, and after that it's up to them.

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Eschew obfuscation, espouse elucidation.

In my efforts to exact and refine something age old accepted, I learned a simple truth. All I had to do after testing for the amusement and satisfaction of a few folks was allow them to leave and pick up my own guitar. I sat quietly alone for about an hour and listened to myself play.
Not once did I set the guitar down and scratch my head in bewilderment as to the accuracy of the pitch my little cedar topped R/W instrument produced.
I'm not a great player, not even a good one. My own arrangements of some Jesse Cook melodies were enough to quench any spark in me that might have caused a need to address afore mentioned temperament.
Truth is, just as Mr. Collins stated. No need to chase the wind, I certainly have no desire to re-invent the wheel. Though I might set mine up with some white walls and polish the chrome a little.
Good words David, I hear you and totally agree.
I have posted off and on today as I decided to take a personal day and just play.

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Nehemiah Covey
www.coveysacoustics.com

Nehemiah, I should add that I can completely identify with your fascination with tuning and temperament, in spite of knowing that it is in some sense chasing the wind.

Though at this point I know there is no "solution", that shouldn't stop anyone from trying. No, I don't believe a universal solution will be found, but the humble exercise of trying can only lead to a better understanding of the dilemma, and prepare one to better deal with it's shortfalls.

People do occasionally find solutions, and with enough pomp they can gain footing and be embraced by the public. This has happened time and time again over many centuries. Each time however, enthusiasm has waned as the solution's shortfalls eventually trickle out. Eventually it may fade from being seen as a glorious answer to our problems, to simply an accepted alternative with slightly different flaws of it's own. That, or it may be abandoned completely, save for small sects of loyal devotees.

I think this is a key point for anyone trying to develop or improve upon a system. The more you educate yourself on the history of intonation and temperament, the better prepared you are to view your own proposals through a clearer lens. It also helps to have studied what is already know and been tried before turning down a well travelled dead end

Still, I would never discourage folks from attempts to improve our system. At the very least it's a wonderful academic exercise, and even if nothing else it will improve your intimate understanding of our 12 tone scale. I am constantly playing with the numbers myself, from real world measurements on strings to purely theoretical mumbo jumbo. The past 3 days I've been working on a spreadsheet related to the BFTS. No new ground being broken here, but it's fun academics and has challenged me to be creative with complex logarithmic and exponential equations. It's fun.





That was a bit of a challenge for me, but laying it out and working out the bugs was a nice refresher course in algebra and Excel.

.

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Eschew obfuscation, espouse elucidation.

David, it's comforting to see I'm not the only builder out there (or in here) spending hours compiling numbers and thinking hard on something that has no doubt been gnawed, chewed, poked, prodded, tweaked, studied and examined to death by many others before me. But that's just how I work I guess. If a semi valid argument can be made on somethings behalf, I take it as a challenge to arrive at my own conclusion regarding it's possibility. I started out in this world that way, learning by doing, so I actually have a lot of stories about many many different experiences in my life, this one will be stored away so that some day when I'm old (and hopefully wise) I'll be able to tell the young whippersnapper what I discovered some time ago. Like my Dad always quipping: "Necessity, the mother of invention, trial the essential teacher".
On a different note though, I have developed a scenario and working test model for what could be charged as a finely adjustable intonation system, after doing a bit of comparing and R&R I settled on this set up. I will have it
fully equipped on a new guitar here soon, so I'll post some photos and results soon. Have to do the legal stuff first. I might add too, this was a well paid venture for me, some folks very curious as to what I'd come up with.
Still, for my own needs and desires for guitar playing, nothing is any better than equal temperament and the complexities of trying to do otherwise doesn't offer reward enough to merit the effort. Be that as it is, I still tried it and now have a much better understanding of this thing we call music.
I also use tail-pieces on flat top acoustics, so some expect this from me.
It's been a pleasure reading your comments Mr. Collins, look forward to more.

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Nehemiah Covey
www.coveysacoustics.com

For the acronym challenged, what is BTFS?

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Howard Klepper
http://www.klepperguitars.com

When all else fails, clean the shop.

Howard;
BFTS is the Buzz Feiten Tuning System, (I think that's how it's spelled)

Fieten or Feiten, either way, it's a system of intonating a guitar that is supposed to bring you closer to proper pitch by having an adjustable nut set up to compensate for flat and sharp notes along the frets.
I'd like to hear your opinion on this also, Howard. PM me if you wnat.

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Nehemiah Covey
www.coveysacoustics.com

I wondered that too Howard. I think it stands for "Buzz Feiten Tuning System" but not sure.

Oops, I think we posted at the same time.

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"After forty-nine years of violin building, I have decided that the search for a varnish is similar to the fox hunt. The fun is in the hunt."
Jack Batts Maker and Repairer of Fine Violins

Howard;
BFTS is the Buzz Feiten Tuning System, (I think that's how it's spelled)

Fieten or Feiten, either way, it's a system of intonating a guitar that is supposed to bring you closer to proper pitch by having an adjustable nut set up to compensate for flat and sharp notes along the frets.
I'd like to hear your opinion on this also, Howard. PM me if you wnat.

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Nehemiah Covey
www.coveysacoustics.com